A Semi-Analytical Approach to Gravity Field Analysis from Satellite Observations

The thesis presents a unified scheme, linking observable gravity field functionals to the gravity field unknowns, the spherical harmonic coefficients. Basic gravity field functionals, incorporated in this scheme, are: low-low satellite-to-satellite tracking (lo-lo SST). This observable is realized through measurement of the range and/or range-rate between two low-flying co-orbiting satellites. high-low satellite-to-satellite tracking (hi-lo SST). This observable is realized by space-borne GPS tracking on board a low-flying orbiter. It results in three-dimensional accurate and continuous orbit determination. satellite gravity gradiometry (SGG). The spatial derivatives of the gravity gradient vector, i.e. the tensor of second spatial derivatives of the gravitational potential, is measured by differential accelerometry over short baselines. The relationship between observables and unknowns is linear in a dual spectral way. The observables are transformed into the Fourier domain. The unknowns are the spherical harmonic spectral coefficients. The model that links these quantities is the so-called lumped coefficient approach. The set of linear relationships---or transfer coefficients---of the lumped coefficient model, together with a stochastic model, allows for an accurate pre-mission error assessment of any type of gravity field mission. The type(s) of observable(s), power spectral error density, orbital parameters, mission duration, and so on, are parameters that can be tuned at will in this procedure. Thus gravity field missions can be planned in advance. One of the advantages of the lumped coefficient approach is the fact that the normal equations, required to infer the unknowns, become a block-diagonal system. In view of the enormous amount of data and of unknowns (e.g. 100000 coefficients), this model leads to a viable way to separate data and unknown, such that computational requirements remain limited. In particular, the thesis describes representations of the gravitational potential, on the sphere and along-orbit, leading to the lumped coefficient model. Then a comprehensive set of transfer coefficients for the above functionals are derived. Next, a spectral analysis follows. Then least-squares error theory is developed. Finally, many case studies display the single and combined effects of the above functionals, and of several other parameters.